[Paper Review] On Convergence and Stability of GANs

Naveen Kodali, Jacob Abernethy+2 more|arXiv (Cornell University)|May 19, 2017

Generative Adversarial Networks and Image SynthesisComputer Science6 references241 citations

TL;DR

The paper reframes GAN training as regret minimization, analyzes non-convex dynamics leading to mode collapse, and introduces DRAGAN, a gradient-penalty method that improves stability and modeling performance across architectures and objectives.

ABSTRACT

We propose studying GAN training dynamics as regret minimization, which is in contrast to the popular view that there is consistent minimization of a divergence between real and generated distributions. We analyze the convergence of GAN training from this new point of view to understand why mode collapse happens. We hypothesize the existence of undesirable local equilibria in this non-convex game to be responsible for mode collapse. We observe that these local equilibria often exhibit sharp gradients of the discriminator function around some real data points. We demonstrate that these degenerate local equilibria can be avoided with a gradient penalty scheme called DRAGAN. We show that DRAGAN enables faster training, achieves improved stability with fewer mode collapses, and leads to generator networks with better modeling performance across a variety of architectures and objective functions.

Motivation & Objective

• Propose a regret-minimization view of GAN training dynamics as an alternative to divergence minimization.
• Analyze convergence in convex-concave versus non-convex GAN settings and identify causes of mode collapse.
• Characterize mode collapse as arising from sharp discriminator gradients around real data points.
• Introduce DRAGAN, a local gradient-penalty method, to mitigate mode collapse and improve stability and modeling performance.

Proposed method

• Model GAN training as a repeated game with no-regret algorithms for both generator and discriminator.
• Provide a theoretical connection between GAN training with alternating gradient updates and regret minimization.
• Analyze non-convex game dynamics to explain possible bad local equilibria and mode collapse.
• Identify sharp discriminator gradients around real data points as a hallmark of mode collapse.
• Propose DRAGAN: a gradient-penalty scheme that constrains discriminator gradients locally around real data, leading to enhanced stability.

Experimental results

Research questions

• RQ1 Can GAN training dynamics be analyzed through regret minimization to explain convergence properties?
• RQ2 What mechanisms underlie mode collapse in non-convex GAN games, and how can they be mitigated?
• RQ3 Does constraining discriminator gradients locally around real data points prevent degenerate local equilibria without harming modeling performance?
• RQ4 How does DRAGAN compare to other gradient-penalty approaches across architectures and objective functions?

Key findings

• Viewing GANs as regret-minimizing games yields convergence insights without requiring the discriminator to be optimal at every step.
• Mode collapse is linked to undesirable local equilibria in non-convex GAN games and to sharp discriminator gradients near real data points.
• DRAGAN’s gradient penalty reduces mode collapse and improves training stability and modeling performance across diverse architectures.
• DRAGAN matches or outperforms state-of-the-art gradient-penalty methods like WGAN-GP in stability while maintaining faster training.
• Local gradient penalties (around real data) are shown to be effective, with broader applicability across different GAN objectives.